admits a Wold-von Neumann type decomposition. In particular, if \(T\)  is assumed to be ananlytic, then it has the wandering subspace property on \(\mathcal {H}\) . It is important to note that operators satisfying any one of the above conditions are always left-invertible. Let us recall some well-known characterizations for general left-invertible operators (see [1]} and it's list of references).
